AMC8 2000

AMC8 2000 · Q12

AMC8 2000 · Q12. It mainly tests Casework, Area & perimeter.

A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long or 1 foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smallest number of blocks needed to build this wall?

一座长 100 英尺、高 7 英尺的砌块墙将使用高 1 英尺、长 2 英尺或 1 英尺的砌块建造（砌块不得切割）。砌块的垂直接缝必须如图所示错开，且墙两端必须平整。建造这座墙需要的最小砌块数是多少？

(A) 344 344

(B) 347 347

(D) 353 353

(E) 356 356

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): If the vertical joins were not staggered, the wall could be build with $\frac{1}{2}(100\times 7)=350$ of the two-foot blocks. To stagger the joins, we need only to replace, in every other row, one of the longer blocks by two shorter ones, placing one at each end. To minimize the number of blocks this should be done in rows 2, 4, and 6. This adds 3 blocks to the 350, making a total of 353.

答案（D）：如果竖直接缝不交错，这堵墙可以用 $\frac{1}{2}(100\times 7)=350$ 块两英尺的砖块砌成。为了让接缝交错，我们只需在每隔一行中，将其中一块较长的砖替换为两块较短的砖，并把它们分别放在两端。为使砖块数量最少，应在第 2、4、6 行这样做。这样在 350 的基础上增加 3 块，总数为 353。

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